Consider a coordinate system (call it number 1) which is represented by a Frame of some kind. Now consider a Mapping which, when applied to the coordinates in system 1 yields coordinates in another system, number 2. The Mapping therefore inter-relates coordinate systems 1 and 2.
Now consider a second Mapping which inter-relates system 1 and a further coordinate system, number 3. If we wanted to convert coordinates between systems 2 and 3, we could do so by:
We are not limited to three coordinate systems, of course. In fact, we could continue to introduce any number of further coordinate systems, so long as we have a suitable Mapping for each one which relates it to one of the Frames already present. Continuing in this way, we can build up a network in which Frames are inter-related by Mappings in such a way that there is always a way of converting between any pair of coordinate systems.
The FrameSet (Figure ) encapsulates these ideas. It
is a network composed of Frames and associated Mappings, in which
there is always exactly one path, via Mappings, between any
pair of Frames. Since we assemble FrameSets ourselves, they can be
used to represent any coordinate systems we choose and to set up the
particular relationships between them that we want.
AST A Library for Handling World Coordinate Systems in Astronomy